Homology Stability for Spaces of Surfaces

Autores: Federico José Cantero Morán
Directores de la Tesis: Carles Casacuberta i Vergés (dir. tes.) , Oscar Randal-Williams (dir. tes.)
Lectura: En la Universitat de Barcelona ( España ) en 2013
Idioma: inglés
Tribunal Calificador de la Tesis: Antonio Félix Costa González (presid.) , Ignasi Mundet i Riera (secret.) , Ulrike Tillmann (voc.)
Enlaces
- Tesis en acceso abierto en: Dipòsit Digital de la UB
Resumen
- In this thesis we study the space of compact connected oriented genus g subsurfaces of a fixed manifold M, and in particular its homological properties. We construct a “scanning map” which compares this space to the space of sections of a certain fibre bundle over M associated to its tangent bundle, and show that this map induces an isomorphism on homology in a range of degrees. Our results are analogous to McDuff’s theorem on configuration spaces, extended from 0-submanifolds to 2-submanifolds.